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document.write( "1. Let the numbers be a < b < c < d < e (in this order/ordering).\r\n" );
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document.write( " Four pair-wise sums of \"a\" with four other numbers are among the given set {16,20,22,23,25,28,29,30,34,37}.\r\n" );
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document.write( " Four pair-wise sums of \"b\" with four other numbers are among the given set {16,20,22,23,25,28,29,30,34,37}.\r\n" );
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document.write( " Four pair-wise sums of \"c\" with four other numbers are among the given set {16,20,22,23,25,28,29,30,34,37}.\r\n" );
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document.write( " Four pair-wise sums of \"d\" with four other numbers are among the given set {16,20,22,23,25,28,29,30,34,37}.\r\n" );
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document.write( " Four pair-wise sums of \"e\" with four other numbers are among the given set {16,20,22,23,25,28,29,30,34,37}.\r\n" );
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document.write( " Therefore, if we sum up all the given numbers, we will get 4*(a+b+c+d+e):\r\n" );
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document.write( " 4*(a + b + c + d + e) = 16+20+22+23+25+28+29+30+34+37 = 264.\r\n" );
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document.write( " It implies that \r\n" );
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document.write( " a + b + c + d + e = 
= 66. (1)\r\n" );
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document.write( "2. Further, 16 is the sum of the two smallest numbers: 16 = a + b. (2)\r\n" );
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document.write( " 37 is the sum of the two largest numbers: 37 = d + e. (3)\r\n" );
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document.write( " It implies (by subtracting (2) and (3) from (1)) that c = 66 - 16 - 37 = 13.\r\n" );
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document.write( " So, we just found one of the five numbers, namely, the middle number c = 13.\r\n" );
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document.write( "3. OK. Let's continue our analysis.\r\n" );
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document.write( " So, the two smallest numbers a and b give the sum of 16, and the third number is 13.\r\n" );
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document.write( " It means that the next sum, 20 (see the condition) is a+c.\r\n" );
document.write( " It can not be nothing else. (Because b + c must be just greater than a + c).\r\n" );
document.write( " If a + c = 20 and c = 13, then a = 20 - 13 = 7. \r\n" );
document.write( " It implies b = 16-7 = 9.\r\n" );
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document.write( " So, the first three numbers are a = 7, b = 9 and c = 13.\r\n" );
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document.write( "4. OK. Now we can make the similar analysis from the other end.\r\n" );
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document.write( " So, the two largest numbers d and e give the sum of 37, and the third number in the descending order is 13.\r\n" );
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document.write( " It means that the next from the largest sum, 34 (see the condition) is e+c.\r\n" );
document.write( " It can not be nothing else. (Because d + c is just less than e + c).\r\n" );
document.write( " If e + c = 34 and c = 13, then e = 34 - 13 = 21. \r\n" );
document.write( " It implies d = 37-21 = 16.\r\n" );
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document.write( "5. Thus the numbers are 7, 9, 13, 16 and 21.\r\n" );
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document.write( " Then their product is 275184.\r\n" );
document.write( "\r\n" ); document.write( "\n" ); document.write( "Answer. The product of the numbers is 275184.\r
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